Yes, with some caveats. If you use FileVault, you need to be able to enter a password before the eGPU activates. I havent used it personally (havent got my eGPU yet) but if you have a display that has multiple inputs, you can run e.g. Mac Mini's native HDMI port to one display, and then from the eGPU to both, so if you need to reboot/cold boot you switch the first display to the HDMI port, login, and then switch back to e.g. the DisplayPort out (or whatever it uses) from the eGPU.
I can't comment on that specific display.
4k on 27" means lower PPI, and IMO it means it's impractical to use the "default" scaling in macOS.
I will be interested in hearing how this works out for you. I tried connecting my Mini with HDMI to a 4K monitor's HDMI port, and then DisplayPort from the eGPU to the same monitor. I was hoping when switching inputs on the monitor that the Mini would detect that there was nothing on that input and not treat it as a third monitor (I am using two). But it would not work well.
Instead of having to disconnect the HDMI from the Mini, I decided to use one display as a secondary monitor hooked up to the Mini's hdmi and my larger 4k monitor hooked up to the eGPU and set as primary. Seems to work a lot nicer for me (I typically don't need to reboot often - but since using this Mini I have had to reboot more than usual due to some hopefully rare issues).